The invention relates generally to interferometers and especially to apparatus and methods for measuring the input phase shift between two interfering waves where the phase shift has been summed with a modulation phase shift, such as one that has been stepped, whose amplitude and phase may be controlled to provide highly stable and wide dynamic range measurements of the input phase balanced in time for additional accuracy.
The analog output of an interferometer represents the combined power of two distinct waves. In general the two waves will interfere resulting in an average power that depends upon the cosine of the phase shift xcex8 between the two waves. The analog output V of a detector, which measures the combined power is given by:
V=Pdc+Pac cos(xcex8)
where, Pdc is an offset and Pac is the gain of the interferometer output. Optical interferometers are the most common devices having this analog output and many utilize fiber optics to guide light waves. In optical sensor applications, an external parameter will proportionally change the phase of one or both of the light waves and the resulting change in the analog output of the light detector of the interferometer is used to sense that parameter. Examples of parameters that can affect the phase of light waves are rotation, pressure and magnetic fields. If R is the input phase shift of the interferometer induced by the parameter and r the phase shift due to other causes, then the analog output is:
V=Pdc+Pac cos(R+r)
This analog output V, must be used in some manner to measure the input phase R to build a useful sensor system. As it normally occurs, the analog output V is not very useful, because it is a nonlinear function of the input phase R, resulting in no output changes and sign ambiguities at many periodic operating points. Also, when R is to be measured with DC accuracy, the offset Pdc obscures the result. Finally, changes in Pdc or Pac within the bandwidth of R corrupt the measurement.
These well known limitations are the reasons that phase modulation is introduced into the system. One embodiment of the present invention is concerned with sinusoid phase modulations that are commonly known as xe2x80x9cPhase Generated Carrierxe2x80x9d or PGC approaches from xe2x80x9cHomodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrierxe2x80x9d, IEEE Journal of Quantum Electronics, October 1982, QE-18, No 10, pp. 1647-1653; Dandridge et al. In such systems, a device is present in the interferometer that introduces a phase shift at a constant frequency resulting in an analog output of:
V(t)=Pdc+Pac cos{R+M sin(t+W)}
where M is the modulation depth of the interferometer, W is the phase of the modulation of the interferometer and t is the linearly increasing time in units of radians. The modulation phase defined by the term:
M sin(t+W)
in the cosine argument is the result of a single frequency sinusoidal drive output applied to the interferometer. The way in which this drive output creates the modulation phase depends on the design of the interferometer. In rotation sensors commonly made out of Sagnac interferometers, the time difference of the sine drive output applied to a phase shifter inside the Sagnac loop gives the modulation. In time domain multiplexed acoustic sensors fabricated from Michelson interferometers, a sinusoidal variation of the light source current will induce wavelength changes which will cause the modulation phase given above. In the simplest modulator case, a fiber wrapped on a piezoelectric cylinder is placed in one arm of a Mach-Zehnder interferometer to transform its sinusoid drive into the modulation phase.
Most approaches to measuring the input phase R in the presence of a sine modulation work with the harmonic series of the analog output given by:
V(t)=Pdc+PacJo(M)cos R                              V          ⁡                      (            t            )                          =                  xe2x80x83                ⁢                              P            dc                    +                                    P              ac                        ⁢                                          J                o                            ⁡                              (                M                )                                      ⁢            cos            ⁢                          xe2x80x83                        ⁢            R                    +                                                  xe2x80x83                ⁢                              2            ⁢                          P              ac                        ⁢            cos            ⁢                          xe2x80x83                        ⁢            R            ⁢                                          ∑                                  k                  =                  1                                ∞                            ⁢                              xe2x80x83                            ⁢                                                                    J                                          2                      ⁢                      k                                                        ⁡                                      (                    M                    )                                                  ⁢                cos                ⁢                                  xe2x80x83                                ⁢                                  (                                                            2                      ⁢                      kt                                        +                                          W                                              2                        ⁢                        k                                                                              )                                                              -                                                  xe2x80x83                ⁢                  2          ⁢                      P            ac                    ⁢          sin          ⁢                      xe2x80x83                    ⁢          R          ⁢                                    ∑                              k                =                1                            ∞                        ⁢                          xe2x80x83                        ⁢                                                            J                                                            2                      ⁢                      k                                        -                    1                                                  ⁡                                  (                  M                  )                                            ⁢              sin              ⁢                              xe2x80x83                            ⁢                              (                                                                            (                                                                        2                          ⁢                          k                                                -                        1                                            )                                        ⁢                    t                                    +                                      W                                                                  2                        ⁢                        k                                            -                      1                                                                      )                                                        
The simplest and most limited open loop interferometric demodulation approach using PGC modulation is where the analog output is mixed with a reference signal equivalent to the frequency used to perform the modulation and lowpass filtered with a gain K to the bandwidth of the input phase R. The resulting analog output is:
V1={2K Pac cos(W1)J1(M)}xc2x7sin R
which may be viewed as a scaling factor in the curly brackets multiplied by the sine of the input phase R. When R has an absolute value less than 0.2 radians, the small angle approximation of sin R=R is valid, resulting in a linear demodulated output over the range of xc2x10.2 radians. The terms that make up the scale factor in the brackets point out the possible demodulation errors, which this simple approach shares with many other methods. The scale factor will change with variations in the interferometer optical gain Pac, the modulation depth M, the synchronous detection phase W and the filter gain K. In the real world applications, where thermal environments may vary by 100 degrees Celsius or more, it is not uncommon to find any one of these scaling terms to change by 10% or more.
Many of those familiar with the art are knowledgeable of these effects and can, through design processes, provide some mitigation of them. For example, two reference frequencies and two synchronous detection channels will add a quadrature output term as follows:
xe2x80x83V2={2K Pac cos(W2)J2(M)}xc2x7cos R
It is evident that, with quadrature measures of the phase, either analog or digital inverse trigonometric post processing may be utilized to determine R. The analog process will be limited in range to xc2x1xcfx80/2 radians; where a digital approach can go much further. If the quadrature terms are digitized, it is possible to implement a processing algorithm such as that defined in U.S. Pat. No. 4,789,240 in a process flow detailed in this patent""s FIG. 7 (starting at the third step) which provides for an extremely large dynamic range, which is limited only by the constraint that the rate of change of phase not exceed xcfx80 radians per consecutive sample. This process initially determines R to within a quadrant or octant, and then using the polarity of the quadrature terms, determines R to within the unit circle, and then using previous sample phase information is able to use simple logic to track phase as it crosses fringe boundaries. This tracking capability is limited only to the bit length of the counter used to track fringe crossings. This design and others like it show promise for large dynamic ranges if implemented in a digital format, but its measurement performance still falls short in that it provides no means of correcting scaling error terms related to modulation depth control, synchronous detector phase errors, and cross channel processing gain variations.
It would be a great improvement to the art if the linear dynamic range of an open loop interferometric demodulator could be arbitrarily large (micro-radians to millions of radians or greater) while it implemented processes, which automatically control all critical scaling factors such that they are invariant. Additionally, such a demodulator should be able to work with many different types of two-beam interferometers, such as Sagnac, Mach-Zehnder, Michelson, Low Finesse Fabry Perot, and others, and be able to efficiently demodulate the multiplexed outputs of such sensors positioned in an array.
There are a number of open loop interferometric demodulation designs described or practiced in the art, which intend to overcome the described scaling errors as well as provide larger linear dynamic ranges. U.S. Pat. Nos. 4,704,032 and 4,756,620 describe approaches which provide active compensation for amplitude scaling, but do not compensate the other scaling errors and additionally provide dynamic ranges less than 1 radian. U.S. Pat. Nos. 4,637,722; 4,687,330; 4,707,136; 4,728,192; and 4,779,975 describe approaches and improvements which compensate for, or are immune to amplitude and phase errors. These implementations also extend dynamic range, but are limited to tens of radians or less. U.S. Pat. No. 5,202,747; 5,289,259; 5,355,216; and 5,438,411 describe approaches and improvements which are immune to amplitude variations and to some degree, modulation depth and gain scaling variations. However these approaches are still subject to phase errors caused by band limited operation of square-law detectors and their associated electronic amplifiers. Additionally, these approaches are limited in dynamic range to less than 100 radians. U.S. Pat. Nos. 4,765,739; 4,776,700; 4,836,676; 5,127,732; and 5,289,257, describe approaches which compensate for, or are immune to modulation depth and amplitude variations and are also capable of operating over large dynamic ranges. However these approaches are still subject to synchronous detection phase offsets and variations (changes in W) and additionally cross-channel gain scaling variations. U.S. Pat. Nos. 4,883,358 and 5,412,472 describe an approach which actively stabilizes field amplitude, modulation depth, and phase errors and is capable of operating over a large dynamic range. However, this approach is still subject to cross channel gain scaling variations.
Although a number of the above referenced design techniques approach the desired high accuracy and large dynamic range design objective, the ones which come the closest require complex electronic circuitry. It would also be a great improvement to the art if an interferometric demodulator having the desired high accuracy and large dynamic range was available, especially if it was simple in design and implementation, and low cost in manufacture. Such traits are inherent in the present invention.
In accordance with the invention, a method and demodulator apparatus is presented to measure the input phase in interferometer systems. The demodulator apparatus is used with phase generated carrier interferometers and includes: an analog to digital converter, which samples the analog output of the interferometer; a clock, which provides the sample and system timing; a digital signal processing apparatus; and a digital to analog converter followed by a lowpass filter, which synthesizes the desired interferometer sine modulation drive output, which creates the phase generated carrier.
Demodulation is accomplished by sampling the interferometer output signal such that quadrature components are extracted and through an inverse trigonometric process, the interferometric phase is measured. The preferred embodiment for the demodulator apparatus involves twelve equally spaced samples taken of the analog output of the interferometer during one modulation period to assure orthogonality (for precise quadrature signal extrication) plus a common interval sample just after the modulation period to assure that the center of the time for the samples is identical. It is recognized that fewer than twelve samples can be taken since some of the twelve samples are normally identical. With the advent of very fast integrated optic devices, which can be used to form the present apparatus, and the fact that most interferometric signals are the result of physical processes, which are relatively slow with respect to sample time, complete symmetry is not always required to assure proper demodulation.
The thirteen digital samples are processed during an expanded modulation cycle in a fast and simple manner to provide the wide dynamic range measurement of the input phase, and the optimum amplitude update of the sine modulation drive output (modulation depth servo), and the optimum phase update of the sine modulation drive output (modulation phase servo). The modulation depth and phase servos are employed to assure an accurate measurement of the input phase.
The dynamic range of the input phase measurement is extended to arbitrarily large values by tracking fringe crossings, which only require that the input phase change by less than xcfx80 radians during the time of one modulation cycle, which is almost a given when high speed components and physical processes are involved.
Therefore, it is an object of the present invention to provide improved open loop demodulation apparatus with a large dynamic range, high accuracy, and low distortion that takes advantage of improved components so that the phase outputs of singular sensors or an array of sensors which can be separated and determined by a single demodulator.
Another object is to reduce the number of samples required to demodulate a phase shifting interferometer output while reducing distortion to a minimum.
Another object is to reduce the cost of apparatus to demodulate the output of multiple interferometers with high accuracy and low distortion.
Another object is to reduce the size and the number of components required to demodulate the outputs of interferometers with high accuracy and low distortion.
These and other objects and advantages of the present invention will become apparent to those skilled in the art after considering the following detailed specification, together with the accompanying drawings wherein: